Electronic Resource
Woodbury, NY
:
American Institute of Physics (AIP)
Chaos
2 (1992), S. 15-17
ISSN:
1089-7682
Source:
AIP Digital Archive
Topics:
Physics
Notes:
A semiclassical analog of the functional equation for the Riemann zeta function is considered. In the case of the zeta function itself, this equation forms the basis for a finite approximation to the Dirichlet series, known as the approximate functional equation. In the same way, the semiclassical functional equation can be shown to give rise to a finite approximation to the semiclassical representation of the quantum spectral determinant as a sum over classical pseudo-orbits. This finite approximation has been called the Riemann–Siegel look-alike formula. The formal nature of the derivation of this result is discussed and the fact that it appears to imply a remarkable relationship between long and short pseudo-orbits is shown.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.165919
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